1. Force and Newton’s Laws
NOTES CH.5
Force and Newton’s Laws

2. 5.1 Force Force: Loosely defined as “pushing” or “pulling.”
forces that require direct contact: pushing a box, hitting a ball, pulling a wagon, and so on.
Some forces, however, can act without direct contact. For example, the gravitational force of the Earth pulls on the Moon even though hundreds of thousands of kilometers separate the two bodies .Electromagnetic forces also do not require direct contact. For instance, two magnets will attract or repel each other even when they are not touching each other.
All forces are vectors: their direction matters.
The net force (the vector sum of all forces on an object) and the object’s mass determine the direction and amount of acceleration.
The SI unit for force is the newton (N). One newton is defined as one kg·m/s2.
Force

3. 5.2 Newton’s first law Law of Inertia
Newton established laws of motion
Newton’s first law: “Every body perseveres in its state of being at rest or of moving uniformly straight forward except insofar as it is compelled to change by forces impressed.”
Newton’s First Law – If there is no net force acting on an object it will continue its state of rest or will continue moving in a straight line at constant speed.
Newton’s laws hold true in an inertial reference frame. An object that experiences no net force in an inertial reference frame moves at a constant velocity or remains at rest.
A car rounding a curve provides an example of a non-inertial reference frame. Newton’s laws would not apply in non-inertial frames.
First Law

4. 5.3 Mass
Mass: A property of an object that determines how much it will resist a change in velocity.
More massive objects require more net force to accelerate than less massive objects. An object’s resistance to a change in velocity is called its inertial mass.
A common error is to confuse mass and weight. Weight is a force caused by gravity and is measured in newtons. Mass is an object’s resistance to change in velocity and is measured in kilograms.
Mass

5. 5.4 Gravitational force: weight
Weight: The force of gravity on an object.
Weight is a force; it has both magnitude and direction. At the Earth' surface, the direction of the force is toward the center of the Earth.
The magnitude of weight equals the product of an object’s mass and the rate of freefall acceleration due to gravity.
Scales are used to measure the magnitude of weight.
Forces like weight are measured in pounds in the British system. One newton equals about 0.225 pounds.
A person with a mass of 100 kg weighs 980 newtons.
Weight

6. 5.5 Newton’s second law: Law of Acceleration
Newton's second law: “A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.” or
Newton’s second law of motion – The effect of an applied force is to cause a body to accelerate in the direction of the applied force. The acceleration is directly proportional to the force and inversely proportional to the mass of the body.
Force =mass x acceleration or F = ma
Force Unit: 1 Kg.m/s2 = 1 Newton (N)
Force of weight (Fw) = mass x gravitational acceleration or
Fw = mg
Acceleration is proportional to the net force on an object inversely and proportional to its mass.
ΣF = ma. The Σ notation means the vector sum of all the forces acting on an object: in other words, the net force.
Both the net force and acceleration are vectors that point in the same direction
2nd law

7.  Sample problems
2nd Law Problem Section Interactive checkpoint: heavy cargo Section 5.8 Interactive checkpoint: pushing a box Section 5.9 Interactive problem: flying in formation

8. Section 5.10 Newton’s third law: Law of Interaction
Newton's third law: “To any action there is always an opposite and equal reaction; in other words, the actions of two bodies upon each other are always equal and always opposite in direction.”
Newton’s Third Law of motion – When one body exerts a force on another, the second body exerts on the first a force of equal magnitude in the opposite direction.
“For every action there is an equal and opposite reaction.
Unaccompanied forces do not exist in nature.” Isaac Newton
Forces come in pairs and that those forces are equal in magnitude and opposite in direction.
Third law

9. 5.11 Normal force
Normal force: When two objects are in direct contact, the force one object exerts in response to the force exerted by the other. This force is perpendicular to the objects’ contact surface.
A normal force is often a response to a gravitational force
Normal forces do not just oppose gravity, and they do not have to be directed upward. A normal force is always perpendicular to the surface where the objects are in contact
Normal Force

10. 5.12 Tension
Tension: Force exerted by a string, cord, twine, rope, chain, cable, etc.
Two assumptions are usually made about the nature of tension.
First, the force is transmitted unchanged by the rope. The rope does not stretch or otherwise diminish the force.
Second, the rope is treated as having no mass (it is massless). This means that when calculating the acceleration of a system, the mass of the rope can be ignored.
Tension

11. 5.13 Newton's second and third laws
The pair of forces in an action-reaction pair acts on different objects.
The weight of an object resting on a surface and the resulting normal force are NOT an action-reaction pair.
Action-Reaction Pairs

12. 5.14 Free-body diagrams
Free-body diagram: A drawing of the external forces exerted on an object.
Free-body diagrams are used to display multiple forces acting on an object
They can be used to determine the magnitudes of forces.
When forces act along multiple dimensions, the forces and the resulting acceleration need to be considered independently in each dimension.
Free-body Diagrams

13. 5.15 Interactive problem: free-body diagram
Interactive problem 5.16 Sample problem: pushing a box horizontally 5.17 Interactive problem: lifting crates

14. 5.18 The Nature of Friction
Friction is a force that resists motion. It involves objects that are in contact with each other and resists the motion of one object sliding past another.
Friction is desirable in many cases (braking) but it can be undesirable as it produces heat and adds to the forces needed to move objects
Friction

15. 5.19 Static friction
Static friction: A force that resists the sliding motion of two objects that are stationary relative to one another or maximum frictional force between stationary objects.
Coefficient of static friction () is the ratio of the force of static friction( Ffsmax) to the normal force ( FN) pressing the surfaces together.
Static friction

16. Characteristics of Friction
Kinetic (sliding) friction – force between objects that are sliding with respect to one another.
Characteristics of friction
Friction acts parallel to the surfaces that are in contact and in a direction opposite to the motion of the object or the net force producing motion
Friction depends on the nature of the materials in contact and the smoothness of the surfaces.
Sliding friction is less than or equal to starting friction
Friction is practically independent of the area of contact
Starting or sliding friction is directly proportional to the forces pressing the surfaces together
Kinetic (sliding) friction

17. Measuring Friction cont…
Coefficient of sliding friction () is the ratio of the force of sliding friction( Ff) to the normal force ( FN) pressing the surfaces together.

18. Changing Friction
We can change the force of friction by changing . Lubricants generally change sliding friction to fluid friction (oils & wax).
Wheels change sliding friction to rolling friction (ball bearings).

19. Solving Friction Problems
Force of friction for an object sliding on a level surface at constant speed can be computed if we know the weight of the object and . Fp= Ff and Fw= FN so Ff =Fw
For objects on an inclined plane we can use the forces of starting and sliding friction to determine if the object will remain at rest, slide down with constant speed, or accelerate down the plane.
If Fp= Ff then it will move at constant speed
If Fp< Ff then it will remain at rest
If Fp> Ff then it will accelerate down the plane
DO THE PRACTICE PROBLEMS IN TEXT!

20. 5.21 Interactive checkpoints
moving the couch 5.22 Sample problem: friction and tension 5.23 Sample problem: a force at an angle 5.24 Interactive problem: forces on a sliding block 5.25 Sample problem: moving down a frictionless plane 5.26 Sample problem: two forces at different angles 5.27 Interactive checkpoint: sledding

21. 5.28 Hooke’s law and spring force
Hooke’s law is used to determine how much force a spring exerts. It states that the amount of force is proportional to how far the end of the spring is stretched or compressed away from its rest point.
Ex. Stretch the end of a spring twice as far from its rest point, and the amount of force is doubled.
The amount of force is also proportional to a spring constant, which depends on the construction of the spring.
A “stiff” spring has a greater spring constant than one that is easier to stretch. Stiffer springs can be made from heavier gauge materials.
The units for spring constants are newtons per meter (N/m).
Hooks law equation Fs=-kx
Hooke's law calculates the magnitude of the spring force. The spring constant is represented by k. The displacement of the end of the spring is represented by x. At the rest position, x = 0. When the spring is stretched, the displacement of the end of the spring has a positive x value. When it is compressed, x is negative.
The equation has a negative sign to indicate that the force of a spring is a restoring force, which means it acts to restore the end of the spring to its rest point. The direction of the force is the opposite of the direction of the displacement.
Hooke's Law

22. 5.29 Sample problem: spring force and tension

23. 5.30 Air resistance
Air resistance: A force that opposes motion in air.
Unlike kinetic friction, air resistance is not constant but increases as the speed of the object increases.
The force created by air resistance is called drag.
Approximating Air resistance
Where:
FD=Drag Force C= Drag coefficient for object
p=air density A= cross-sectional area v=velocity
Terminal velocity is the maximum speed an object reaches when falling. The drag force increases with speed while the force of gravity is constant; at some point, the upward drag force equals the downward force of gravity. When this occurs, there is no net force and the object ceases to accelerate and maintains a constant speed.

24. 5.31 Interactive summary problem: helicopter pilot